Simulation-based engineering and science, including topology design, parameter optimization, and uncertainty quantification, are usually characterized by high-dimensional systems that require immense computational costs. Despite significant advancements in computer hardware and the development of GPU parallel computing over the past few decades, real-time simulations of large-scale, high-dimensional systems remain intractable with conventional methods (e.g., finite element analysis). Regarding that, model order reduction/reduced order modeling methods offer efficient and powerful tools for addressing large-scale, high-dimensional problems by reducing the size of the computational models while maintaining accurate solutions in a fast and efficient manner. This mini-symposium provide a platform for researchers to exchange insights on the development and applications of model order reduction methods. Topics of interest include but not limited to: model order reduction techniques for high-dimensional problems; low-rank representations, tensor decomposition and proper generalized decomposition; space-time-parameter reduced-order methods; nonlinear model reductions; error estimates and parameter adaptivity; implementation on large-scale engineering problems, topology optimization, uncertainty quantification, operator learning and inverse problems. Additionally, potential topics may include integrated machine learning methods and data-driven simulations.